# Involution

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## involution

[‚in·və′lü·shən]
(biology)
A turning or rolling in.
(embryology)
Gastrulation by ingrowth of blastomeres around the dorsal lip.
(mathematics)
Any transformation that is its own inverse.
In particular, a correspondence between the points on a line that is its own inverse, given algebraically by x ′ = (ax + b)/(cx-a), where a 2+ bc ≠ 0.
A correspondence between the lines passing through a given point on a plane such that corresponding lines pass through corresponding points of an involution of points on a line.
(medicine)
The retrogressive change to their normal condition that organs undergo after fulfilling their functional purposes, as the uterus after pregnancy.
The period of regression or the processes of decline or decay which occur in the human constitution after middle life.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

## Involution

(raising to a power), an algebraic operation consisting in repeating a quantity a n number of times:

The number a is the base of the power, n is the exponent, and an is the power. For example, 3x3x3x3 = 34 = 81. The second power of a number is called its square and the third power, its cube.

## Involution

(regression), in biology, a reduction or loss, in the process of evolution, of certain organs, and a simplification of their organization and functions (for example, various degrees of intestinal reduction in certain parasitic worms and arthropods). Degenerative changes in protozoans and bacteria caused by unfavorable conditions in the habitat are also called involutional. In medicine, the term sometimes refers to atrophy of organs and tissues, such as in aging.

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.
References in periodicals archive ?
If A is a finite dimensional n-Lie algebra with an involutive derivation D, then we have
Hence, [DELTA] is not involutive. According to the Frobenius theorem, SBMS has been shown to be a nonholonomic system.
Notice that an involutive EQ-algebra L satisfies [logical not] [logical not]x = x for all x [member of] L.
The second identity shows that [X,Y] [member of] [T.sub.[lambda]], proving that [T.sub.[lambda]] is involutive.
involutive, or hyperintegrated; rather than picking up the rhythm of the
of Sao Carlos, Brazil) synthesize the major results from the past 25 years of developments in the theory of involutive systems of complex vector fields.
Their relation was almost an equivalence relation, and was defined on the set of frames whose Gramian matrices lie in a solid, inverse closed, involutive Banach algebra.
If N(N(x)) = x, for all x [member of] L, then N is called an involutive negator.
(8) Lone appearance of a tricola poetic form at the palistrophe's core recalls Roland Meynet's observation that Hebrew rhetoric is often involutive, cohering concentrically "around a centre which is the focal point, the keystone, through which the rest finds cohesion.
The later pieces were all for B clarinet, including Lied by Luciano Beria, Clair by Franco Donatoni or Involutive by Paul Mefan.
Tomasi's first movement of concerto (Edition Leduc); and a piece for clarinet solo composed by either Donatoni's Clair (Edition Ricordi), Singier's Bouts rimes burines (Edition Lemoine), Rieunier's Distances (Edition Salabert), Mefano's Involutive (Edition Salabert) or Gaussin's Satori (Edition Leduc).

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